Numbers and operations · Ages 13–14
Simplifying surds worksheet
Part of: Surds & irrational numbers
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Simplifying surds worksheet
Numbers and operations · Ages 13–14
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.24 × 54 =
Answer:
2.In simplest form: 294 =
Fill in each blank
Answer:
3.In simplest form: 24 =
Fill in each blank
Answer:
4.72 ÷ 2 =
Answer:
5.In simplest form: 42 × 24 =
Fill in each blank
Answer:
6.In simplest form: 280 =
Fill in each blank
Answer:
7.In simplest form: 18 × 12 =
Fill in each blank
Answer:
8.126 =
Answer:
Part B: Choose, or true or false (2 marks each)
9.252 = 67
True or false?
Answer:
10.What is 192 in simplest form?
- A. 643
- B. 83
- C. 38
- D. 412
Choose the right answer
Answer:
11.Which number is the largest?
- A. 52
- B. 15
- C. 45
- D. 26
Choose the right answer
Answer:
12.76 = 294
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A rectangle is 28 cm long and 112 cm wide. What is its area?
Working:
Answer:
14.A square has an area of 72 cm². Its perimeter in simplest surd form is ab cm. What is a + b?
Working:
Answer:
15.A square has an area of 320 cm². Which of these is the length of each side?
- A. 58 cm
- B. 320 cm
- C. 645 cm
- D. 85 cm
Choose the right answer
Working:
Answer:
16.Ka-lok says 46 and 144 are equal. Ka-lok is right.
True or false?
Working:
Answer:
17.Simplify 567. Put the steps in order.
- A. 81 × 7 = 97
- B. 567 = 81 × 7
- C. 81 × 7 = 81 × 7
Write the letters in the right order
Working:
Answer:
18.Simplify 243: the biggest perfect square that divides 243 is , so 243 = .
Fill in each blank
Working:
Answer:
Show the answers and working
Simplifying surds worksheet: Answers and working
Part A: Working out and filling in
1. 36
24 × 54 = 24 × 54 = 1296 = 36.
2. 7, 6
294 = 49 × 6, 49 the biggest square factor: 294 = 49 × 6 = 76.
3. 2, 6
24 = 4 × 6, 4 the biggest square factor: 24 = 4 × 6 = 26.
4. 6
72 ÷ 2 = 72 ÷ 2 = 36 = 6.
5. 12, 7
42 × 24 = 1008, and 1008 = 122 × 7, so 127.
6. 8, 5
80 = 45, so 280 = 2 × 45 = 85.
7. 6, 6
18 × 12 = 216, and 216 = 62 × 6, so 66.
8. 864
12 = 122, so 126 = 122 × 6 = 864.
Part B: Choose, or true or false
9. True
252 = 62 × 7, so 252 = 67.
10. B. 83
192 = 64 × 3, the biggest square factor 64: 192 = 83.
11. C. 45
26 = 24, 52 = 50, 45 = 80; compare those with 15 under the root.
12. True
To bring 7 back under the root, square it: 76 = 72 × 6.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 56 cm²
Area = 28 × 112 = 28 × 112 = 56 cm².
14. 26
Side = 72 = 62, perimeter = 4 × 62 = 242, so a + b = 24 + 2 = 26.
15. D. 85 cm
Side = 320 = 64 × 5 = 85 cm.
16. False
46 = 42 × 6: 4 goes back under the root squared.
17. B → C → A
Split off the biggest square factor, 81, use ab = a × b, then take its root: 97.
18. 81, 9, 3
243 = 81 × 3 and 81 = 9, so 243 = 93.
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